Answer:
T = 995.95 N
Explanation:
Using the equation to find the tension in the wire
2* T * sin (φ) = m * g
T = m∙g / (2∙sin(φ))
cos(φ) = d/l ⇒ d = l∙cos(φ)
we know the angle of thew "hot" wire as φ₀ = 3°
d = l₀∙cos(φ₀)
α = 23×10⁻⁶K⁻¹ thermal expansion coefficient of aluminum
So the length changes to
l₁ = l₀ - ∆l = l₀∙(1 - α∙∆T)
Since distance d does not change, the angle decreases such that:
d = l₁∙cos(φ₁) = l₀ * (1 - α * ∆T) * cos(φ₁)
l₀∙cos(φ₀) = l₀ * (1 - α * ∆T) * cos(φ₁)
φ₁ = cos⁻¹ ( cos(φ₀) / (1 - α * ∆T) )
φ₁ = cos⁻¹ ( cos(3°) / (1 - 23×10⁻⁶K⁻¹ * 20.0 C) )
φ₁ = 2.4457°
T = 85.0 N / (2 * sin (2.4457°) )
T = 995.95 N
